The phase singularity, a sudden phase change occurring at the reflection zero is widely explored using various nanophotonic systems such as metamaterials and thin film cavities. Typically, these systems exhibit a single reflection zero with a phase singularity at a specific incident angle, particularly at larger angles of incidence (>50 degrees). However, achieving multiple phase singularities at a single incident angle remains a formidable challenge. Here, the existence of a dual‐phase singularity is experimentally demonstrated at a lower incident angle using a tunable Tamm plasmon polariton (TPP) cavity that consists of gold‐coated ultralow‐loss phase change material Sb2S3‐based distributed Bragg reflector. It can excite narrowband TPP resonances from normal incidence to a wide angle of incidence for both s‐ and p‐polarizations of light. Notably, this TPP cavity shows dual‐phase singularity at lower angles of incidence since the excited TPP for s‐ and p‐polarizations exhibits zero reflection at slightly different wavelengths for the same incident angle. A TPP cavity‐based scalable hydrogen sensor is proposed and shows that the dual‐phase singularity can further improve the sensitivity of singular phase‐based sensing approaches. Moreover, spectrally tunable dual‐phase singularity is experimentally demonstrated at a lower incident angle using a metal‐free Tamm cavity.